When stormy weather threatened to overturn the small boat late Saturday night, an Iraqi Kurd on board called his brother in France.
Although he was about 2,000 kilometres (1,250 miles) away and spoke only broken French, the 33-year-old brother went to the police station in Poissy, in the western suburbs of Paris, and alerted the authorities with the help of a friend who translated, police said.
"In the reception area the gentleman was met by a patrolwoman who, despite the oddness of the situation, took the matter seriously and immediately gave the alert," said Poissy police commissioner Yann Bessette.
Officers on duty raised the alarm with maritime authorities in southeastern France, who passed the message along to Greece.
The migrants were rescued and taken to a Greek island to await transport to Athens, Bessette said he had been told.
Greek authorities on Sunday rescued a boat carrying 31 migrants of unknown nationality, including four children, off the island of Cephalonia, a maritime official in Greece told AFP. It was not immediately possible to confirm if this was the same boat.